Solution Properties of Architecturally Complex Multiarm Star Diblock

Article pubs.acs.org/Macromolecules

Solution Properties of Architecturally Complex Multiarm Star Diblock Copolymers in a Nonselective and Selective Solvent for the Inner Block Jesse L. Davis,† Xu Wang,† Kamlesh Bornani,† Juan Pablo Hinestrosa,† Jimmy W. Mays,† and S. Michael Kilbey, II*,†,‡ †

Department of Chemistry and ‡Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States S Supporting Information *

ABSTRACT: In comparison to the behavior of linear block copolymers, much less is known about the structure and properties of highly branched polymeric materials. Motivated by this, the solution properties of a series of 26- and 40-arm polystyrene−poly(2-vinylpyridine) (PS−PVP) star diblock copolymers of different weight-average molecular weight (Mw) and styrene to 2-vinylpyridine (S/V) ratios are studied. These stars are investigated in tetrahydrofuran (THF), a thermodynamically good solvent for both blocks, and in toluene, a solvent that is selective for the inner PS blocks. It is found that in both THF and toluene, the 26- and 40-arm stars remain dispersed as unimolecular star block copolymers across the concentration range studied, 0.001< c < 10.0 mg/mL. The hydrodynamic radius, Rh, increases with PS Mw and number of arms, with the stars of highest Mw and number of arms having the largest Rh. The characteristic ρ ratio, Rg/Rh, is ∼1.0, suggesting that these stars do not behave as homogeneous hard spheres, but rather exhibit Gaussian soft sphere characteristics. TEM images indicate that these stars adopt an unusual asymmetric structure in toluene due to intramicellar microphase segregation of the arms: The PVP blocks collapse and aggregate within the unimolecular structure while the PS blocks stretch and shield the aggregated PVP domain. Despite the strong tendency of PVP to drive aggregation in toluene, repulsive steric interactions between solvated PS blocks and this rearrangement prevent PVP domains of selectively solvated stars from assembling into multimolecular aggregates. This morphological behavior is consistent with inferences drawn from analyses of the concentration dependence of the z-average diffusion coefficient, which suggests that frictional interactions are stronger than star−star interactions. In total, these results shed new light on how topologically complex, amphiphilic block copolymers organize in solution.

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INTRODUCTION Amphiphilic (“dual loving”) block copolymers (ABCs) are macromolecular analogues of surfactants that contain solvophobic and solvophilic blocks that are linked by covalent bonds. For example, polystyrene−poly(2-vinylpyridine) (PS−PVP) diblock copolymers are archetypal ABCs: when dissolved in a selective solvent such as toluene, which is thermodynamically good for PS but poor for PVP, PS−PVP diblock copolymers can undergo microphase separation, creating micellar ensembles by self-assembly. The size and shape of the aggregate depend on the sizes of the constituent blocks, with spherical, cylindrical, and vesicular structures forming due to the tendency of the blocks to microphase segregate in the selective solvent.1 The insoluble PVP blocks segregate to the inside, or core, of the micelle in a PS-selective solvent, while the soluble PS blocks remain in contact with the solvent, forming the corona of the micelle. Micellization of block copolymers occurs at or above the critical micelle concentration (CMC), and in the absence of specific, directional intermolecular forces, the assembly is driven by a balance of repulsive interactions between stretched, © XXXX American Chemical Society

solvated blocks of the corona, the desire of the nonsolvated blocks to minimize contact with the solvent, and the cost of creating an interface between the soluble and insoluble blocks.2 There are two main models that describe micellization. The first is the open association model, which describes the formation of micelles with no unimers in solution. However, this model is rarely appropriate in surfactant-like systems because it suggests that a CMC does not exist: the amphiphilic copolymers readily aggregate, forming structures with no welldefined number of chains (thus leading to a distribution of aggregate sizes). The second, the closed association model, describes the formation of micellar structures at and above the CMC with thermodynamic equilibrium established between those well-defined aggregates and single chains that are present in solution.3,4 The spontaneous generation of complex, well-organized structures from polymeric building blocks in which domain Received: January 5, 2016 Revised: February 17, 2016

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DOI: 10.1021/acs.macromol.6b00024 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules Table 1. Macromolecular Properties of 26- and 40-Arm Star Diblock Copolymers sample IDa

PDI

S/V

c (mg/mL)

[PS50−PVP50]26 [PS102.5−PVP20.5]26 [PS103.8−PVP11.5]26 [PS53.8−PVP53.8]40 [PS106.3−PVP21.3]40 [PS108−PVP12]40

1.23 1.45 1.36 1.26 1.16 1.30

1 5 9 1 5 9

2.49 2.47 2.48 2.32 2.48 2.47

[PS103.8−PVP11.5]26 [PS106.3−PVP21.3]40

1.36 1.16

9 5

3.06 2.06

Rh,appb (nm)

Rh,appc (nm)

D0d (cm2/s)

Rh,0d (nm)

toluene 38 57 56 52 79 71

50 59 59 61 85 79

8.18 7.01 7.38 6.63 4.63 4.99

10−8 10−8 10−8 10−8 10−8 10−8

48 56 53 59 85 79

60 72

59 78

8.99 × 10−8 5.97 × 10−8

54 81

× × × × × ×

THF

a

The multiarm star copolymers are referred to as [PSmPVPn]f, where f is the number of arms and the subscripts m and n refer to the molecular weight (Mw) of the PS and PVP blocks in thousands, respectively. bRh,app calculated from Ds values obtained from the slope of the best-fit line of Γ versus q2 at c = 2.5 mg/mL. cRh,app calculated from ⟨D⟩z values, which are obtained by extrapolating to zero scattering angle the best-fit line through light scattering data plotted as Γ/q2 versus q2 at c = 2.5 mg/mL. dDiffusion coefficient and hydrodynamic radius found by extrapolation to c = 0.

light scattering. Two of the solvents used were good solvents for both blocks; another two were chosen such that each was selective for one of the blocks; and the final two were chosen so that they were isorefractive solvents with one of the individual blocks. The authors suggested that the highly stretched polystyrene blocks formed the corona of the star, whereas the polyisoprene blocks formed the core with the overall morphology displaying segregation between PS and PI domains. Furthermore, studies in isorefractive solvents (chlorobenzene and bromoform, which are isorefractive good solvents for polyisoprene and polystyrene, respectively) showed that the blocks microphase segregated strongly, with the inner PI core being of similar geometric dimension to its corresponding 18-arm homopolyisoprene star.21 It has been demonstrated that the number of arms and block composition can also affect the self-assembly behavior of architecturally complex star block copolymers. Strandman et al. investigated the properties of poly(methyl methacrylate)-bpoly(acrylic acid) (PMMA-b-PAA) amphiphilic 8-arm and 4arm star block copolymers in aqueous solution. A combination of simulation and experimental techniques was used to investigate the effects of salt, pH, ionic strength, and arm number on the self-assembly. The critical aggregation concentration (cac) of the stars was dependent on the length of the hydrophobic PMMA block. Stars with longer hydrophobic blocks had a lower cac, and the aggregation number was dependent on the number of arms. Below the cac and in the absence of added salt, the stars existed as unimolecular micelles. The addition of salt caused a morphological transition in the 4arm stars from spherical to wormlike aggregates. However, this phase transition was not observed with the more crowded 8arm stars due to the shielding effect of its arms.22−24 With the knowledge that composition and architecture (geometric constraints) caused by attaching numerous arms about a central junction impact the self-assembly behavior of ABCs, we investigate the solution phase behavior of six PS− PVP star diblock copolymers in a thermodynamically nonselective good solvent for both blocks and in a solvent that is selective for the inner PS block. These stars have different Mw due to their systematic variation in styrene to 2-vinylpyridine ratio, S/V, at two different number of arms. In our previous study focused on the structures adopted when ABCs of different architecture, size, and composition are mixed, we characterized these six stars by DLS at the single concentration used for mixed self-assembly.25 Here we use a combination of

sizes, properties, and interactions can be varied by the choice of monomers used and finely controlled by tailoring block sizes and relative volume fractions has found use in the medical and chemical industries. For example, spherical micelles and vesicles are candidates for the delivery of drugs in the fight against diseases, such as cancer.4−6 In this application, ABCs enhance drug solubilization/stabilization, and the encapsulation alters the pharmacokinetic profile, providing a way to control drug release.7 ABCs may also find application in environmental remediation because they can solubilize contaminants present after an environmental disaster, such as an oil spill.8 ABCs can also be used to form patterned surfaces for microelectronics and bit-patterned media as well as to pattern catalytic sites.9,10 While the volume fraction, degree of polymerization, and interaction energies dominate the morphological phase behavior of ABCs, architecture (topology) also affects selfassembly.3,11 Because of recent advances in living polymerization techniques, architecturally complex star diblock copolymers and homopolymers with numbers of arms ranging from 3 to greater than 100 have been synthesized with low polydispersities.12−14 In comparison to an enormous number of studies focused on linear ABCs, there are few reports on solution and surface self-assembly properties of multiarm star diblock copolymers.15−21 Highly dense multiarm star block copolymers have the unusual ability to form thermodynamically stable unimolecular constructs in solution.11,16 They also possess superior mechanical and rheological properties as compared to their linear counterparts of similar weight-average molecular weight (Mw).17 Amphiphilic star block copolymers are architecturally different from heteroarm and miktoarm stars. Heteroarm and miktoarm stars consist of two (or more) distinctly different types of homopolymer arms emanating from a single core, with heteroarm stars having an equal number of arms of each monomer type while miktoarm stars are asymmetric in the number of arms of each type.18 Amphiphilic star block copolymers have arms consisting of covalently linked amphiphilic blocks joined at a central core, which governs their self-assembly behaviors.11,19 There are only a few reports of amphiphilic star block copolymers with a large number of arms having been studied in solution and at surfaces.11,20 With respect to varying solvent conditions, Nguyen et al. investigated two high molecular weight 18-arm star block copolymers with arms of polyisoprene-b-polystyrene diblock copolymers (from here on, the inner block is named first) in six different solvents at 35 °C by B


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initial sampling time of 125 ns. The polymer solutions, each approximately 1.5 mL, were contained in previously cleaned, dustfree 10 mm borosilicate glass cuvettes that were sealed with a Teflon cap. A counting time of 600 s was used at each angle, and as the concentration decreased, the counting time was increased in order to obtain reliable statistics. DLS data were analyzed following protocols described in our previous report,27 which are summarized in the Supporting Information. Light scattering experiments were replicated at least once to ensure validity of results. Two different methods were used to find concentration-dependent diffusion coefficients and hydrodynamic radii. In the first method, zaverage diffusion coefficients, ⟨D⟩z, are obtained from the q2 = 0 intercept of a plot of Γ/q2 versus q2, where Γ is the characteristic decay rate determined from analysis of the light intensity autocorrelation function at a given scattering angle and q is the scattering wave vector.28,29 The diffusion coefficient determined in this way is the zaverage over the molar mass distribution30 and reflects translational diffusion of the star (no contributions due to rotation or segmental fluctuations) at a given concentration. Because of the finite concentration, the hydrodynamic radius determined using the Stokes−Einstein relation is an apparent hydrodynamic radius, Rh,app: Rh,app = kT/6πη0⟨D⟩z. Here k is the Boltzmann constant, T is the absolute temperature, and η0 is the solvent viscosity (0.555 cP for toluene and 0.454 cP for THF).28 In the second method, the solution diffusion coefficient, Ds, is determined from the slope of the plot of Γ versus q2, and the corresponding apparent hydrodynamic radius also can be calculated using Ds and the Stokes−Einstein relation. Two methods of calculating mutual diffusion coefficients Ds and ⟨D⟩z are used simply to provide perspective on how the different fitting methods impact characteristic properties of the star block copolymers. The effect of concentration on ⟨D⟩z is described using the equation29

dynamic and static light scattering (DLS and SLS) and transmission electron microscopy (TEM) to elucidate solution structure and self-assembly behaviors as a function of macromolecular design in a systematic fashion as a function of concentration and solvent type.

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EXPERIMENTAL SECTION

Materials. Multiarm star block copolymers were synthesized via anionic polymerization using custom-built, all-glass reactors with break-seals. While details on the synthesis of these block copolymers can be found in our early publication,26 they are outlined briefly here. In short, the synthesis is a two-step, living anionic polymerization process, first involving synthesis of a multifunctional oligo(styryl)lithium-grafted poly(divinylbenzene) core, from which styrene is anionically polymerized in benzene at room temperature, followed by crossover to polymerize 2-vinylpyridine in tetrahydrofuran (THF) at −78 °C. This synthetic approach yields polystyrene-b-poly(2-vinylpyridine) star block copolymers with outer PVP blocks that form the corona and that are covalently linked to the inner PS blocks. The samples were characterized by a combination of multiangle laser light scattering, 1H NMR, and elemental analysis,26 and the results are summarized in the first three columns of Table 1. Throughout this paper, including in the tables and figures, the multiarm star copolymers are referred to as [PSmPVPn]f , where f is the average number of arms and the subscripts m and n refer to the molecular weight (Mw) of the PS and PVP blocks, in thousands, respectively. The styrene to 2vinylpyridine ratio (S/V) is also reported. It is important to appreciate that the synthetic approach of using a multifunctional, anionic initiating core from which the arms are grown and using fractionation to purify the stars naturally leads to a product that is disperse in terms of block length distributions, numbers of arms, and, potentially, core size. Thus, even though we capture design variations through m, n, f, and S/V and one can calculate the Mw by the product f(m + n), these are average measureswe expect the samples to be more heterogeneous even though anionic methods are used. In addition, this accounting does not consider the contribution of the oligostyrene−divinylbenzene core, which is known to be disperse.26 THF (99%) and toluene (HPLC grade) were purchased from Alfa Aesar and used as received. Block Copolymer Solution Preparation. Stock solutions of the PS−PVP star block copolymers in THF or in toluene were prepared gravimetrically by adding solvent, filtered through 0.2 μm PTFE filters (Millipore), to bulk copolymer that was weighed into previously cleaned, dust-free vials. These stock solutions were equilibrated at room temperature for at least 5 days. Then, 24 h prior to a light scattering experiment, an aliquot was taken from the stock solution, transferred into a previously cleaned vial, and diluted with filtered solvent (0.2 μm PTFE) to create a solution of the desired concentration. Concentrations examined ranged from nominally 0.001 to 10.0 mg/mL. A total of five concentrations were studied. Characterization by Light Scattering and Theory. Static and dynamic light scattering (SLS and DLS) measurements were performed on a four-detector, goniometer-based ALV system equipped with a linearly polarized 22 mW HeNe laser operating at a wavelength, λ, of 632.8 nm. The instrument is mounted on an optical table to reduce the effects of vibrations. The incident beam is reflected by two mirrors, and any increased scattered intensity that may occur is reduced by a liquid crystal attenuator before being analyzed by a builtin quadrant photodiode equipped with a beam splitter plate. The laser light is then focused into the sample cell that is positioned in the center of the scattering cell, which is filled with toluene. The scattering cell is mounted on a motor-driven precision goniometer (±0.01°) equipped with four detectors interleaved by 34° from one another. A maximum of nine different goniometer angles were used in the DLS experiments, giving rise to signal detection at scattering angles ranging from 20° to 146°. The temperature of the scattering cell is maintained at 25 ± 0.1 °C in all experiments by circulating a mixture of water and ethylene glycol through the cell jacket. The signal is processed using a fast photon count digital correlator (ALV-7000 multiple tau) with an

⟨D⟩z = D0(1 + kDc + ...)

(1)

Here kD is the diffusion virial coefficient, which takes into account the polymer−polymer thermodynamic interactions and the polymer− polymer hydrodynamic interactions.29 D0 is the diffusion coefficient at infinite dilution, or the self-diffusion coefficient, and it is obtained by extrapolating the concentration-dependent ⟨D⟩z values to c = 0. The concentration-independent, or true, hydrodynamic radius, Rh,0, is obtained from the corresponding D0 value using the Stokes−Einstein relation. SLS experiments were performed using several scattering angles between 20° and 146° that were accessed by using nine goniometer angles. Toluene was used as the calibration standard. A “dust-filter” option of 3% was utilized for the measured scattered intensity at each scattering angle, and three runs of 10 s each were averaged. If the average count rate for any of the 10 s runs at any scattering angle differs by more than 3% from the ensemble average, the set of three measurements was repeated until the criterion of deviating by less than 3% of the ensemble average is satisfied. The z-average radius of gyration, Rg ≡ [⟨S2⟩z]1/2, was determined using the truncated form of the virial expansion for the scattered intensity:28

Kc 1 = + 2A 2 c ΔR M w,appP(q)

(2)

Here ΔR is the normalized absolute scattering intensity, which is calculated according to28

ΔR = (Isolution − Isolvent)

Iabs,std Istd

(3)

ΔR takes into account the contribution of light scattered from the solvent, Isolvent, and the absolute scattered intensity of the standard, Iabs,std, which is normalized by the intensity for a scattering standard, Istd. A2 is the second virial coefficient, and c is the solution concentration. K is the contrast factor, which is defined as28 C


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Macromolecules Table 2. Results from Static Light Scattering Measurements on 26- and 40-Arm Star Diblock Copolymers sample ID

S/V

dn/dca (mL/g)


1 5 9 1 5 9

0.104 0.097 0.106 0.107 0.106 0.085

[PS103.8−PVP11.5]26 [PS106.3−PVP21.3]40

9 5

0.176 0.192

Rgb (nm) toluene 46 53 50 56 75 79 THF 40 75

A2 (cm3 mol/g2) 5.2 5.5 2.3 3.9 3.1 3.9

× × × × × ×

10−5 10−5 10−5 10−5 10−5 10−5

1.2 × 10−5 1.7 × 10−5

Mw,appc (g/mol)

ρd

× × × × × ×

106 107 106 107 107 107

0.96 0.95 0.94 0.95 0.88 1.00

1.25 × 107 5.33 × 107

0.74 0.93

4.35 2.05 7.87 1.07 5.70 1.13

Measured at λ = 658 nm. bRg determined from Zimm analysis using at least two different concentrations. cApparent molecular weight, Mw,app, determined from SLS experiments. dThe ρ ratio is defined as ρ = Rg/Rh,0.

a

Figure 1. (A) Light intensity autocorrelation functions for the 26-arm stars and (B) the 40-arm stars in toluene at c = 2.5 mg/mL at a scattering angle of 88°. (C) Apparent hydrodynamic radii, Rh, distributions for the 26-arm stars and (D) the 40-arm stars at c = 2.5 mg/mL and a scattering angle of 88°. The colors and symbols assigned here are used consistently in other plots presenting data from DLS measurements in toluene. The stated concentration of 2.5 mg/mL is a nominal valueactual values are stated in Table 1.

K=

2 16π 2 2⎛⎜ dn ⎞⎟ n λ 4NA ⎝ dc ⎠

Characterization by Transmission Electron Microscopy. To prepare samples for imaging by transmission electron microscopy (TEM), a pipet was used to dropcast a small amount of polymer solution onto the carbon film grid, and the films were allowed to dry. Because of the rapid solvent evaporation and the high glass transition temperature, Tg, of PS (104 °C) and PVP (105 °C), the native morphology in solution is expected to be preserved.31 Before imaging, the sample was stained by exposure to iodine vapor for 24 h, which renders the PVP microdomains dark in the images. Because carbon film grids were used, to facilitate imaging the entire structure, selected samples were also stained using ruthenium tetroxide (RuO4), which stains both PS and PVP domains.32 In addition, to provide contrast between the PS and PVP domains and the solid carbon film, we dissolved gold(III) chloride trihydrate in the star block copolymer

(4)

Here NA is Avogadro’s number, λ = 632.8 nm, and n is the solvent refractive index. The refractive index increment, dn/dc, was determined at λ = 658 nm using a Wyatt OptiLab Rex differential refractometer. dn/dc values determined for each of the stars are presented in Table 2. For comparatively small particles, generally characterized by the criterion q2Rg2 ≪ 1, P(q) can be expressed as28 P(q) = 1 −

q 2R g 2 3

(5) D


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Figure 2. Mean decay rates, Γ, versus q2 for the (A) 26-arm stars in toluene at c = 2.5 mg/mL and for the (B) 40-arm stars in toluene at c = 2.5 mg/ mL. For plots A and B the solution diffusion coefficient, Ds, is obtained from the slope of the best-fit lines. The data, when recast as Γ/q2 versus q2, allow ⟨D⟩z to be obtained for the (C) 26-arm stars in toluene at c = 2.5 mg/mL and the (D) 40-arm stars in toluene at c = 2.5 mg/mL by extrapolating the best fit line to q2 = 0. The dependence of Γ/q2 with respect to q2 for all samples suggests that in a selective solvent for the inner block the star diblock copolymers do not behave as hard spheres. The concentrations stated here are nominal valuesactual values are given in Table 1. solution and stirred for 24 h. The solution was subsequently dropcast and stained on the carbon film grid using RuO4. Au3+ preferentially interacts with the PVP domains, rendering it darker than the PS blocks due to the formation of gold nanoparticles under the electron beam during TEM imaging.33 Images were acquired at column temperature using a Zeiss Libra 200 MC transmission electron microscope. A Gatan UltraScan US1000XP CCD camera was used to record the images using the Digital Micrograph software package.

shown in Figures 1C and 1D, respectively. In Figure 1C, stars [PS50−PVP50]26, [PS103.8−PVP11.5]26, and [PS102.5−PVP20.5]26 show broad distributions and the peak shifts to higher Rh as the total Mw of the star block copolymers increases. Figure 1D shows three relatively narrow distributions for the 40-arm stars with peaks for samples [PS106.3−PVP21.3]40 and [PS108− PVP12]40 overlapping, which indicates similar hydrodynamic sizes (size distributions) for these two high Mw 40-arm stars having medium and high S/V ratios. While it is possible to force the fitting to yield two narrower (but overlapping distributions), given the aforementioned heterogeneity of the stars imparted by the synthesis and purification methods, it seems unreasonable to do so.34 Figures 2A and 2B show the fits of the mean decay rate, Γ, versus q2 for each of the 26-arm and 40-arm stars, at c = 2.5 mg/mL in toluene. Because the light intensity autocorrelation functions for the star copolymers are well-fit with a singleexponential decay function, there is a single decay mode that displays a linear dependence on the scattering wave vector, as shown in Figures 2A and 2B. The slight upturn at high q is a result of the high Mw of the stars.34 Best-fit lines intersect the yaxis at Γ ≈ 0, which suggests that the particle motion is governed solely by diffusive processes.35 As a result, the slope of the line for each star yields the solution diffusion coefficient, Ds, and from each value, the corresponding Rh,app can be calculated

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RESULTS AND DISCUSSION Hydrodynamics of Architecturally and Compositionally Diverse Star Copolymers. The solution properties of the three 26-arm and the three 40-arm stars with varying block lengths and styrene to 2-vinylpyridine (S/V) ratios in the range of 1 ≤ S/V ≤ 9 were investigated by laser light scattering. Figures 1A and 1B show the normalized light intensity autocorrelation function for all of the stars at c = 2.5 mg/mL in toluene, which is a preferential and thermodynamically good solvent for the PS blocks. The decay of the autocorrelation function depends markedly on the size of the scattering particles, and in this case, the light intensity autocorrelation functions are well-fit by a single-exponential decay function, which suggests that there is only one population of scatterers in solution for each star. The normalized amplitude distribution functions for the 26-arm and 40-arm stars at c = 2.5 mg/mL are E


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Figure 3. Zimm plots for star [PS103.8−PVP11.5]26 in toluene, a selective solvent for the inner PS blocks (left), and in THF, a nonselective good solvent (right). Properties determined from the extrapolations to zero scattering angle, q2 = 0, and to zero concentration, c = 0, are set above each Zimm plot.

S/V ratio are known to micellize25 because of the unfavorable interaction between PVP and toluene, the absence of aggregation is somewhat surprising. It suggests that the outer PVP blocks are not able to “stick” stars together. This finding raises questions about the morphological arrangement of the arms in the selective solvent. This point will be addressed where results of TEM imaging are presented. Each of the star block copolymers was investigated by SLS, and representative results are shown in Figure 3, which displays the Zimm plots created for [PS103.8−PVP11.5]26 in the PSselective solvent toluene (left) and in the nonselective good solvent THF (right). Zimm plots for all of the other stars are available in the Supporting Information. Because the intensity of the scattered light is proportional to the molecular weight of the scattering particle and (dn/dc)2,36 SLS provides an absolute measurement of the apparent weight-average molecular weight, Mw,app. The Mw,app, Rg, and A2 values obtained from a series of SLS experiments at different concentrations (at least two) and at numerous scattering angles37 are presented in Table 2. From Table 2 it should be noted that the Mw,app, Rg, and A2 are of the same order of magnitude in both THF and toluene, which along with the hydrodynamic radii shown in Table 1 suggest that the amphiphilic star diblock copolymers remain as isolated, unimolecular stars in a selective solvent as well as in a thermodynamically good solvent for both blocks. Given that replicate scattering experiments were performed, discrepancies between molecular weights calculated based on the average number of arms and block sizes and those based on multiple extrapolations performed in the Zimm analysis are attributed to the combination of scattered intensity being dominated by larger scatters within an admittedly polydisperse population of star block copolymers as well as sensitivities of the SLS analyses and the simplifying assumptions inherent to calculated star molecular weights, which were described earlier. In view of these factors, the agreement between calculated molecular weight and those extracted from scattering is rather respectable. SLS yields similar Rg values for the 26-arm stars, with [PS50− PVP50]26 having the smallest Rg value, followed by [PS103.8− PVP11.5]26 and [PS102.5−PVP20.5]26. This pattern of behavior is consistent across the 40-arm stars, where the Rg of [PS53.8− PVP53.8]40 is 1.4 times smaller than the Rg of stars [PS108− PVP12]40 and [PS106.3−PVP21.3]40. This trend is a direct result of the Mw,app and the S/V ratio: [PS50−PVP50]26 has the smallest Rg because it has the smallest Mw,app and S/V ratio, while

using the Stokes−Einstein relation. The R h,app values determined by this method are given in Table 1 (column 5). The second method of treating DLS data to extract diffusion coefficients and hydrodynamic radii provides additional insight into the behavior of these complex macromolecular amphiphiles. The slope of the best-fit line through the data plotted as Γ/q2 versus q2 (at 36 different scattering angles) for each of the 26-arm and 40-arm stars (shown in Figures 2C and 2D) suggests slight deviation from homogeneous hard-sphere diffusive behavior because of the small but noticeable qdependence over the angular range studied.27 The angular dependence also suggests nonrigid particles whose internal motions vary from the center of mass.30 This subtle but important characteristic of the solution behavior of the stars will be revisited in a later section. The values of the Rh,app obtained from ⟨D⟩z are reported in Table 1. From the plots in Figure 2, it is evident that the 26-arm stars diffuse at a faster rate than the 40-arm stars, and as the total Mw of the stars increases, the stars diffuse at a slower rate, which suggests larger hydrodynamic radii. The two methods of data fitting, using either the slope from Γ versus q2 or the q2 = 0 intercept of Γ/q2 versus q2, can yield different apparent hydrodynamic radii, as observed by comparing Rh,app values reported in Table 1. The 26-arm star [PS50−PVP50]26, which has an S/V ratio of 1, shows the largest difference in Rh,app as a result of the two fitting methods. The Rh,app values calculated for the other star block copolymers by the two methods are otherwise consistent. Because the method of Γ/q2 versus q2 is more sensitive to dust, noise, and other sources of error, the true Rh at infinite dilution was calculated from ⟨D⟩z values obtained at various concentrations studied. These results are presented and discussed in a later section. The hydrodynamic radii calculated for stars [PS103.8− PVP11.5]26 and [PS106.3−PVP21.3]40 in THF at a concentration of 3.06 and 2.06 mg/mL, respectively, are given in Table 1. When dissolved in THF, a thermodynamically good solvent, it is expected that both of the blocks are well solvated and resist aggregation. However, it is observed that the [PS103.8− PVP11.5]26 and [PS106.3−PVP21.3]40 star block copolymers have similar hydrodynamic radii in both the selective and the nonselective good solvents used here. This behavior suggests that even in a solvent selective for the inner PS blocks, these stars are not forming multimolecular aggregates in solution. In view of the fact that PS−PVP diblock copolymers of this size or F


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Macromolecules [PS102.5−PVP20.5]26 has the largest Mw,app (and an S/V = 5). These results suggest that molecular weight of the PS block defines the size of the individual stars. The 26- and 40-arm stars of S/V = 1, which have PS block sizes of nominally 50 kDa, clearly are smaller than the stars having PS block sizes that are nominally 100 kDa. The large difference in Rg between the 40arm stars and the 26-arm stars is due to the dense topology of the macromolecule. Because of the large number of arms, size and solution self-assembly is dominated by microphase separation and interarm repulsion. Some insight into the shape of the stars also can be gained from light scattering. The ρ ratio (≡ Rg/Rh,0) for each star in toluene is close to 1.0, which agrees with Burchard’s prediction for dense stars38 and also indicates Gaussian soft sphere behavior rather than hard sphere behavior.30 In THF, star [PS103.8−PVP11.5]26 has a ρ ratio of 0.74, which suggests homogeneous hard sphere behavior.30 These results point to the possibility that the stars with diblock copolymer arms have morphologies that depend on solvent type, number of arms, and S/V ratio. Further discussion of the morphological structure is reserved until results of TEM imaging are presented. Concentration Study. The effect of solution concentration on the size of the star block copolymers was examined using light scattering measurements, and the results are presented in Figure 4. Figure 4A shows the concentration dependence of Rh for the 26- and 40-arm stars in toluene. For all samples, ranging from low (c ≈ 0.001 mg/mL) to high concentration (c ≈ 5.5 mg/mL), the Rh remains at values consistent with the conclusion that these stars form unimolecular micelles in toluene, resisting aggregation as the concentration is increased due to the shielding effects brought about by the large number of arms.39 Because these systems maintain this characteristic over a wide range of concentration, it suggests that amphiphilic star block copolymers are promising candidates as nanocarriers for a variety of applications.40 There appears to be a slight decrease in ⟨D⟩z over the concentration range studied, as reflected by the data presented in Figure 4B. Values of D0 were extracted from the c = 0 intercept of the best-fit line according to eq 1, and kD values were obtained from the slope. These values are presented in Tables 1 and 3, respectively. The linear coefficient of the virial expansion, kD, is often defined as kD = 2A2Mw − kf, where kf characterizes the frictional drag that opposes the motion of the molecule.41 kD can be used to gain insight into the relative balance of thermodynamic and frictional interactions between polymer and solvent; however, care must be exercised in interpreting values for the unimolecular star block copolymers in a selective solvent using framework developed for homopolymer solutions. For these stars in toluene, the small but negative kD values could be interpreted as suggesting poor solvent conditions due to attractive interactions between the stars;35,42,43 however, the DLS measurements give no indication of aggregation, and as Lodge et al. note43 from their studies of micellar systems, chain stretching can reduce repulsive interactions relative to those expected for free chains. Indeed, A2 values measured for all of these diblock stars in toluene are positive but smaller than those typically reported for PS homopolymers.44 An alternative interpretation of the finding that kD values of the stars in toluene and for star [PS103.8−PVP11.5]26 in THF are less than 0 is that kf is greater than 2A2Mw, implying that frictional interactions are stronger than thermodynamic star−star interactions. This behavior has also been observed for PI and

Figure 4. Dependence of Rh on concentration for 26- and 40-arm stars in toluene (A). Dependence of ⟨D⟩z on concentration for 26- and 40arm stars in toluene (B). Comparison of the concentration dependence of Rh for samples [PS103.8−PVP11.5]26 and [PS106.3− PVP21.3]40 in toluene and THF (C). The solid lines in (B) are fits to the data obtained from eq 1 while the dashed lines in (A) and (C) are trend lines to guide the eye.

PS homopolymer stars in good solvents.45,46 For star [PS106.3− PVP21.3]40 in THF, the kD value is small but positive, which suggests good solvent conditions and that the thermodynamic star−star interactions are greater than frictional interactions. While the former is clearly the case, we refrain from speculating as to whether the concentration dependence of this star in THF is truly different from behavior of the star block copolymers in toluene (and star [PS 103.8 −PVP 11.5 ] 26 in THF) or if G


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Macromolecules Table 3. Hydrodynamic and Frictional Interactions for 26and 40-Arm Star Diblock Copolymers sample IDa

S/V


1 5 9 1 5 9

[PS103.8−PVP11.5]26 [PS106.3−PVP21.3]40

kD (mL/mg)

toluene −1.12 × 10−2 −2.65 × 10−2 −4.42 × 10−2 −7.88 × 10−3 −5.72 × 10−4 −4.41 × 10−3 THF 9 −3.44 × 10−2 5 +4.74 × 10−3

kf (mL/mg) 0.464 2.27 0.408 0.840 3.55 0.834 0.334 1.81

uncertainties in values of kD, A2, and Mw,app arising because of the weak concentration dependence of scattered intensity are influencing the result. It is worth noting that the kf values show an interesting dependence on the design of the star block copolymers: In toluene and THF, stars of S/V = 5 exhibit greater frictional interactions (kf) than stars of S/V = 1 and S/V = 9, and the 40-arm stars have larger kf values compared to their 26-arm analogues. The effect of concentration on hydrodynamic size, Rh, in selective and nonselective solvents was investigated for two selected stars, [PS103.8−PVP11.5]26 and [PS106.3−PVP21.3]40, and the results are shown in Figure 4C. For these 26- and 40-arm stars, there is a very small concentration dependence in both toluene and THF that is more pronounced for the smaller star. Rg values were determined from SLS measurements to investigate the effect of branching, Mw, and S/V ratio as a function of concentration, and these results are shown in Figure S6 (Supporting Information). Characteristic sizes extracted from both DLS and SLS measurements provide insight into how design of the star block copolymer affects size. Measured Rh values (Figure 4A) and Rg values (see Supporting Information) show that star size depends most strongly on overall Mw and number of arms, suggesting that as the arms are diblocks of uniform Mw and composition, crowding induced by the number of arms dominates the size of the stars. TEM. The morphology of the star block copolymers was investigated by TEM using staining techniques involving I2, RuO4, and a combination of RuO4 and Au(III) stainings, which together can be used to identify the microstructural arrangement of PVP and PS blocks of the star block copolymers. Figure 5 displays TEM images of the [PS50−PVP50]26 and [PS53.8−PVP53.8]40 star block copolymers dropcast from toluene on copper-supported carbon film grids. Figure 5A shows an image of [PS53.8−PVP53.8]40 stained with I2. From this image it appears that the star block copolymers do not have hard sphere morphologies previously inferred from light scattering measurements by Roovers et al. for highly dense 64- and 128-arm homopolymer stars in a good solvent.47 Rather, the PS−PVP star block copolymers studied here adopt oblate shapes in a selective solvent, with a characteristic diameter of ∼30 nm. The image also confirms these stars remain as isolated macromolecules in solution. Figure 5B, acquired after I2 staining, shows that [PS50−PVP50]26 stars dropcast from toluene also adopt this structure with a diameter of ∼20 nm. While I2 stains PVP only, the overall structure of [PS53.8−PVP53.8]40 sample cast from toluene solution is revealed when RuO4 is used to stain both PS and PVP blocks.48 From Figure 5C we can see that the entire star has a diameter of ∼60 nm, which is

Figure 5. TEM images of (A) the 40-arm star [PS53.8−PVP53.8]40, and (B) the 26-arm star [PS50−PVP50]26 dropcast from toluene solutions with PVP blocks stained by iodine vapor. TEM image of (C) [PS53.8− PVP53.8]40 dropcast from toluene solution with both PS and PVP blocks stained using RuO4. TEM image of doubly stained (D) [PS53.8− PVP53.8]40 deposited from a toluene solution containing gold(III), which coordinates with PVP blocks. The dried film is subsequently exposed to RuO4 vapors. This double staining method renders the PVP blocks darker than the PS blocks, as described in the text. Based on this series of images, a drawing (inset) of how the stars rearrange in toluene, a selective solvent for the PS (red) blocks, is developed.

consistent with light scattering results. Once again, it appears that the stars are not spherical in shape but slightly oblate. To clearly identify where the PVP blocks are in relation to the PS blocks and to investigate the degree of microphase separation between the two incompatible blocks, a double staining technique using gold(III) chloride trihydrate and RuO4 was used. The mechanism of gold(III) chloride trihydrate staining of PVP is described by Spatz et al.31 An image of [PS53.8−PVP53.8]40 stained in this fashion is shown in Figure 5D. Here the RuO4 stained PS blocks appear lighter than the gold-coordinated PVP blocks that have higher electron density compared to the PS blocks: Regions containing PVP are marked by a cluster of tiny dark spots, which are generated by the reduction of gold ions by the electron beam during exposure.31 The lighter regions that surround the PVP blocks are the RuO4 stained PS blocks, which otherwise would not be visible because of their low electron density.33 From the image, it is seen that the PVP end blocks collapse and aggregate within a region of the star, while the PS blocks stretch to remain in contact with the solution. In so doing, the PS chains shield the PVP blocks from the solvent, forming a type of asymmetric structure that is depicted in the cartoon inset in Figure 5D. The identification of a segregated morphology driven by intramolecular microphase separation that result in PVP blocks collapsing in the inner region seems surprising given the high level of geometric constraint in these star diblock copolymers. Conceptually, it might be reasonable to expect that the poorly solvated PVP blocks would simply collapse upon their contour length, segregating at the PS/PVP interface, or possibly bury H


Macromolecules

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ACKNOWLEDGMENTS Support for this work from the National Science Foundation (Award No. 1131252) is gratefully acknowledged. Aspects of the microscopy work were facilitated by a program supported by the U.S. Army Research Office through Grant No. W911NF-11-1-0417. Access to light scattering capabilities is enabled by the User program of the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory, by the Department of Energy, Office of Science. Professor Paul Russo is thanked for helpful discussions and advice.

themselves within the star, either individually or by clustering PVP blocks from neighboring chains, as ways to minimize contact with toluene. However, both of these possibilities would lead to more unfavorable contacts between PVP segments and either PS segments or solvent toluene than if multiple PVP blocks were able to “find” each other and segregate themselves from toluene or PS segments. The structure in which PVP blocks are collapsed but at the periphery of the structure would seem to invite multistar aggregation, which is not evident from the analyses of light scattering data or TEM images. Thus, the type of structure implied by the image produced using dual staining (Figure 5D) and depicted in the inset cartoon would allow the stars, particularly those with long PVP blocks, to remain isolated due to repulsive intermolecular interactions between the wellsolvated PS blocks that shield the PVP domain. This structural behavior also would seemingly lead to reduced frictional interactions between the stars.

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CONCLUSIONS The solution properties of six architecturally complex 26- and 40-arm star block copolymers of varying molecular weight and S/V ratio have been investigated. DLS and SLS experiments suggest that highly dense, architecturally complex stars with a large number of arms resist aggregation in solution with the overall molecular weight and the large number of arms dictating their solution properties. Basic physical and thermodynamic properties were measured, and the phase behavior of the macromolecular structure was established in a selective and nonselective good solvent. The intramolecular interactions dominate the solution self-assembly and phase behavior of high molecular weight multiarm star block copolymers, helping to keep the stars isolated and minimizing hydrodynamic interactions between stars. It is possible that these behaviors are enabled by an unusual intramolecular rearrangement that allows long PVP blocks to be shielded, rather than collapsed, and decorating the outer periphery of the star. These studies highlight the notions that the behaviors of topologically complex amphiphilic block copolymers differ in unexpected ways from the behaviors of their linear analogues and offer new and unusual structures by self-assembly. From a practical point of view, these results suggest that high molecular weight and highly branched star block copolymer systems may be advantageous when used as nanocarriers because they remain disperse and do not disassemble as they are diluted. ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b00024. Description of DLS analysis, Zimm plots of the other stars in toluene and in THF, TEM images in THF acquired with different stainings (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (S.M.K.). Notes

The authors declare no competing financial interest. I


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Solution Properties of Architecturally Complex Multiarm Star Diblock

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